{"id":"https://openalex.org/W2963010131","doi":"https://doi.org/10.1093/logcom/exx007","title":"OUP accepted manuscript","display_name":"OUP accepted manuscript","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2963010131","doi":"https://doi.org/10.1093/logcom/exx007","mag":"2963010131"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exx007","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exx007","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal Of Logic And Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/2117/111902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083651367","display_name":"Argimiro Arratia","orcid":"https://orcid.org/0000-0003-1551-420X"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Arratia, Argimiro","raw_affiliation_strings":["Department of Computer Science / BGSMath, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","*Department of Computer Science / BGSMath, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science / BGSMath, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"*Department of Computer Science / BGSMath, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ortiz, Carlos E.","orcid":null},"institutions":[{"id":"https://openalex.org/I51204116","display_name":"Arcadia University","ror":"https://ror.org/00ff4bt20","country_code":"US","type":"education","lineage":["https://openalex.org/I51204116"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ortiz, Carlos E.","raw_affiliation_strings":["Department of Computer Science and Mathematics, Arcadia University, USA Email:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Mathematics, Arcadia University, USA Email:","institution_ids":["https://openalex.org/I51204116"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I51204116"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28622496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6492375135421753},{"id":"https://openalex.org/keywords/residue","display_name":"Residue (chemistry)","score":0.5438088178634644},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5170174837112427},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5035786032676697},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4980010986328125},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4941544830799103},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.46243536472320557},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45045214891433716},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.4279623031616211},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3949001431465149},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14242452383041382},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10256749391555786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6492375135421753},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.5438088178634644},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5170174837112427},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5035786032676697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4980010986328125},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4941544830799103},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.46243536472320557},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45045214891433716},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.4279623031616211},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3949001431465149},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14242452383041382},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10256749391555786},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/logcom/exx007","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exx007","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal Of Logic And Computation","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/111902","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/111902","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/111902","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/111902","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W112858668","https://openalex.org/W142911782","https://openalex.org/W1542908046","https://openalex.org/W1575886793","https://openalex.org/W1729076678","https://openalex.org/W1967218884","https://openalex.org/W1985056301","https://openalex.org/W2029957918","https://openalex.org/W2036656440","https://openalex.org/W2045583484","https://openalex.org/W2060270693","https://openalex.org/W2063991224","https://openalex.org/W2070678975","https://openalex.org/W2088141885","https://openalex.org/W2092230546","https://openalex.org/W2127493538","https://openalex.org/W2165293955","https://openalex.org/W2326876290","https://openalex.org/W2327233892","https://openalex.org/W2398918824","https://openalex.org/W2431007515","https://openalex.org/W2894888219","https://openalex.org/W4233712846","https://openalex.org/W4236835455","https://openalex.org/W4409010003"],"related_works":["https://openalex.org/W2394594825","https://openalex.org/W1651031009","https://openalex.org/W4288101869","https://openalex.org/W3148574779","https://openalex.org/W2140913328","https://openalex.org/W3021792919","https://openalex.org/W2064409016","https://openalex.org/W4252518165","https://openalex.org/W4233354377","https://openalex.org/W2367640509"],"abstract_inverted_index":{"Separations":[0],"among":[1],"the":[2,18,53,59,70,76,107,114,133,162,174],"first-order":[3],"logic":[4,77,131,163],"|${\\cal":[5,158],"R}es(0,+,\\times)$|":[6],"of":[7,20,40,42,50,55,61,78,109,111,117,148,151,153,164],"finite":[8,45,79,118,134,165],"residue":[9,46,80,119,135,166],"classes,":[10],"its":[11],"extensions":[12,83],"with":[13,168,173],"generalized":[14],"quantifiers,":[15],"and":[16,52,82,171],"in":[17,26,113,126,157],"presence":[19],"a":[21,130,139],"built-in":[22,169],"order":[23,170],"are":[24,84,123,179],"shown":[25,125],"this":[27,127,149],"article,":[28],"using":[29],"algebraic":[30],"methods":[31,37],"from":[32,93],"class":[33],"field":[34],"theory.":[35],"These":[36],"include":[38],"classification":[39],"spectra":[41,110,152],"sentences":[43,112,154,180],"over":[44,58,132],"classes":[47,81,91,101,136,167],"as":[48],"systems":[49],"congruences,":[51],"study":[54],"their":[56],"|$h$|-densities":[57],"set":[60],"all":[62],"prime":[63],"numbers,":[64],"for":[65,129],"various":[66],"functions":[67],"|$h$|":[68],"on":[69],"natural":[71],"numbers.":[72],"Over":[73],"ordered":[74],"structures,":[75],"known":[85],"to":[86,95,105,137],"capture":[87],"|$\\mathbf{DLOGTIME}$|-uniform":[88],"circuit":[89,99],"complexity":[90,100],"ranging":[92],"|$\\mathbf{AC}^0$|":[94],"|$\\mathbf{TC}^0$|\u2060.":[96],"Separating":[97],"these":[98],"is":[102,155],"directly":[103],"related":[104],"classifying":[106],"|$h$|-density":[108],"corresponding":[115],"logics":[116],"classes.":[120],"General":[121],"conditions":[122],"further":[124],"work":[128],"have":[138,183],"sentence":[140],"whose":[141,181],"spectrum":[142,182],"has":[143],"no":[144,184],"|$h$|-density.":[145],"A":[146],"corollary":[147],"characterization":[150],"that":[156],"R}es(0,+,\\times,<)":[159],"+":[160],"\\mathbf{M}$|\u2060,":[161],"extended":[172],"majority":[175],"quantifier":[176],"|$\\mathbf{M}$|\u2060,":[177],"there":[178],"exponential":[185],"density.":[186]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2019-07-30T00:00:00"}
